Near-Field Scattering Tomography Systems for Object Imaging and Material Characterization
Safieddin Safavi-Naeini and Jeffery Orchard (Computer Science)
Electromagnetic inverse scattering based permittivity profile estimation is one of the most promising techniques for imaging and material characterization. However, since electromagnetic inverse scattering problems are ill-conditioned, ill-posed, and not unique, electromagnetic inverse scattering has not yet been successfully implemented in many potential application areas, particularly in clinical imaging. This dissertation presents an effective implementation procedure, a new formulation, and a novel concept to alleviate these problems and hopefully shorten the gap between the current state-of-the-art and real applications and to improve the electromagnetic inverse scattering technique in general.
The first major contribution of this dissertation is introducing a new planar nearfield scattering tomography (PNFST) system. The proposed PNFST system is the first scattering tomography system implemented at the W-band frequency range to overcome the multipath effects in free space. The transmitting antenna in the proposed system remains stationary throughout the measurement while the receiving antenna scans the measurement plane. By keeping the transmitting antenna location and orientation fixed, the incident field remains unchanged in the proposed system; instead, the object undertest (OUT) orientation is changed by utilizing a rotational stage and illuminating the OUT from different angles. Eliminating the multipath effects in the system enable us to make the incident field measurement process fast and quite effective since the field is measured in the absence of the scatterer only once.
The second major contribution of this dissertation is formulating the electromagnetic inverse scattering problem based on a discrete modal analysis. To do so, the scattered electric field and the volume equivalent current source (VECS) are projected into a subspace spanned by the singular vectors obtained from the spatial Green’s function of the nearfield scattering tomography system representation. Differentiating between the significant singular values and the less significant one is an important step. The scattered electric field coefficients are bounded and stable while the VECS coefficients are not stable in the new subspaces since the singular values of the Green’s function modal representation start decaying very fast beyond a certain threshold (ill-conditioning). Minimizing the mean square error of the estimated scattered electric field or the estimated permittivity profile is used to find the threshold. The singular vectors below the threshold is considered as the ii radiating singular vectors, so the VECS projected into the radiating singular vectors are called the radiating VECS, and the permittivity profile is calculated through the radiating VECS are called the radiating permittivity prole. The experimental results show that the boundary of OUT is effectively determined by using the radiating part of either the permittivity profile or the conductivity profile of the region of interest.
The third and foremost contribution of this dissertation is proposing a novel concept for solving the electromagnetic inverse scattering problem to make the solution unique by introducing the non-radiating contrast factor and the non-radiating objective function. Decomposing the permittivity into two complementary parts, the radiating permittivity prole and the non-radiating permittivity prole, improves the ill-posedness nature of the electromagnetic inverse scattering problem. Since the radiating permittivity prole is visible, and the non-radiating permittivity prole is invisible from the view point of the outside observer, in the first step, the boundary of the OUT is determined by using the radiating permittivity prole obtained from the measurement outside the OUT. Then, we estimate – with sufficient accuracy – the permittivity profile of the OUT by minimizing the non-radiating objective function while applying the boundary information.